A simple theorem to generate exact black hole solutions

TL;DR

This paper proves a theorem that generates a two-parameter family of exact static, spherically symmetric black hole solutions under specific energy-momentum tensor conditions, extending to include the cosmological constant.

Contribution

It introduces a simple theorem that characterizes a broad class of exact black hole solutions with potential extensions to cosmological settings.

Findings

The theorem encompasses known exact solutions within these symmetries.

Discussion on asymptotic behavior and regularity of solutions.

Extension of the theorem to include the cosmological constant.

Abstract

Under certain conditions imposed on the energy-momentum tensor, a theorem that characterizes a two-parameter family of static and spherically symmetric solutions to Einstein's field equations (black holes), is proved. A discussion on the asymptotics, regularity, and the energy conditions is provided. Examples that include the best known exact solutions within these symmetries are considered. A trivial extension of the theorem includes the cosmological constant {\it ab-initio}, providing then a three-parameter family of solutions.